Tomography entails detecting radiation that traverse a slice of a subject at multiple angles and reconstructing properties of the sample from the detected radiation. If the source of radiation is within the subject, the technique is referred to as emission tomography. For example, positron emission tomography (PET) and single photon emission computed tomography (SPECT) are used in medical imaging in which gamma rays emitted from within the patient are detected. If the source of radiation is outside the subject, such as in x-ray computed tomography (CT) the technique is referred to as transmission tomography. CT is used in medical imaging, as well as geological sample, such as fossils, reservoir rocks, and soil.
After the radiation is detected, a reconstruction algorithm is applied to the detector data to build a model of the sample scanned. Analytical techniques, such as filtered back projection, are based on a single reconstruction, whereas iterative techniques use multiple repetitions of an algorithm that converges toward an improved solution.
Iterative techniques include Algebraic Reconstruction Technique (ART), Simultaneous ART, Simultaneous iterative reconstruction technique (SIRT), Ordered subset SIRT, Multiplicative algebraic reconstruction technique, Maximum likelihood expectation-maximization, Ordered subset expectation-maximization, Ordered subset convex algorithm, Iterative coordinate descent (ICD), Ordered subset ICD, or Model-based iterative reconstruction.
X-ray CT has been used to map the internal structure of geological samples. Typically, the sample is irradiated, and a reconstruction algorithm characterizes the attenuation of volume elements that make up the sample. Volume elements or voxels having similar properties can then be grouped or “segmented” to define a structural element, such as a pore or a crystal phase.
A segmentation process can be performed at the end of one iteration of the reconstruction algorithm, to separate the volume into common material clusters. Then each cluster is processed in the forward model of the next iteration of the reconstruction to verify the integrity of the “combination of segmented data” with the acquisition.
CT can be performed uses a source or multiple sources that provide x-rays of more than one frequency. Information about attenuation at different frequencies can provide additional information about the sample, which may be useful for many purposes such as to segment the sample into different materials. Some dual-energy iterative reconstruction/segmentation have been proposed in the past.
One method provides employs the same segmentation for each cluster obtained from the original dataset. For example, suppose the segmentation extracts four clusters. By a dual iterative reconstruction/segmentation algorithm, one obtains both four sub-sinograms and four tomograms (one for each cluster). The four tomograms allow quantitative analysis (volumetric measurements, for instance), and since each is linked to its sinogram, one can also extract attenuation, Hounsfield windowing, and dose or radiation checking (in PET, or radiotherapy) directly from the projections. Further, since each cluster tomogram is supposed to be composed of one single “material”, some methods reconstruct each voxel value as the amount of material which appears in the voxel, for example:voxel=1−>100% of the voxel contains the material of this cluster.voxel=0.34−>34% of the voxel contains the material of that cluster.
That is particularly helpful when one wants to vectorize the tomogram for 3D rendering. Since there is a dual checking between tomographic reconstruction and segmentation, a multi-material voxel will appear in several tomograms. In other words: the kind of “mixture of voxels” is verified during the iterations of the algorithm in order to check that the segmentation is consistent with the acquisition itself.
But, in these approaches, the segmentation is based on the intensity of the reconstructed voxels and on the local variation of intensities to determine the interfaces between clusters. In other words, such segmentation is based primarily on image characteristics.